+1 sessions
Median return -0.20%Completed observations: 13
- Middle 50%
- -3.33% … +3.72%
- Positive returns
- 38%
MARA Holdings · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
MARA Holdings's latest move against its own history.
MARA Rare
+30.91%
+2.90σ
About once every 41 trading sessions
31 comparable moves / 1,258 observations
What happened afterwards
All history-qualified moves of at least 2.5σ. Results after the event are descriptive statistics, not trading instructions.
+7 sessions
Median return +2.33%Completed observations: 13
- Middle 50%
- -5.43% … +27.78%
- Positive returns
- 62%
+30 sessions
Median return +18.62%Completed observations: 13
- Middle 50%
- -36.83% … +122.40%
- Positive returns
- 62%
Every rare move, in context
Instrument: MARA (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 12 Jan 2023 | +2.90σ | +30.91% | About once every 41 trading sessions31 comparable moves / 1,258 observations | +9.25% | +25.18% | +1.14% |
| 4 Jan 2023 | +3.42σ | +24.12% | About once every 74 trading sessions17 comparable moves / 1,258 observations | -7.35% | +81.99% | +70.85% |
| 21 Nov 2022 | -2.85σ | -17.14% | About once every 39 trading sessions32 comparable moves / 1,258 observations | +3.72% | +0.32% | -36.83% |
| 19 Jul 2022 | +2.94σ | +32.17% | About once every 40 trading sessions30 comparable moves / 1,204 observations | -3.33% | +2.33% | -10.62% |
| 7 Jul 2022 | +3.09σ | +24.07% | About once every 44 trading sessions27 comparable moves / 1,196 observations | +21.40% | +39.23% | +122.40% |
| 9 May 2022 | -3.56σ | -19.20% | About once every 72 trading sessions16 comparable moves / 1,156 observations | -2.32% | -15.89% | -44.12% |
| 15 Nov 2021 | -4.17σ | -27.03% | About once every 86 trading sessions12 comparable moves / 1,036 observations | -0.05% | -5.43% | -38.79% |
| 8 Nov 2021 | +2.92σ | +17.99% | About once every 38 trading sessions27 comparable moves / 1,031 observations | +1.05% | -32.34% | -54.28% |
| 26 Jul 2021 | +3.79σ | +20.05% | About once every 74 trading sessions13 comparable moves / 957 observations | -8.65% | -2.91% | +33.16% |
| 8 Feb 2021 | +3.37σ | +42.41% | About once every 53 trading sessions16 comparable moves / 841 observations | +17.21% | +27.78% | +18.62% |
| 30 Nov 2020 | +3.19σ | +46.73% | About once every 40 trading sessions20 comparable moves / 794 observations | -1.43% | -23.89% | +266.24% |
| 23 Nov 2020 | +4.43σ | +45.13% | About once every 113 trading sessions7 comparable moves / 790 observations | -0.20% | +20.12% | +354.47% |
| 17 Nov 2020 | +3.31σ | +25.00% | About once every 52 trading sessions15 comparable moves / 786 observations | -6.77% | +38.06% | +236.77% |
The number has a method behind it
Sigma measures the size of a log return relative to volatility estimated before the period. Rarity is counted from actual historical standardized moves, not inferred from a normal distribution.
σt = ln(Ct / Ct−1) / vtvt ← t−1, t−2, …
Volatility adapts to the market regime with EWMA (λ = 0.94 for daily and weekly observations). Current-period returns are excluded. Each historical σ uses its own prior volatility.
Both directions count toward rarity. Reference history spans up to five years. A period with no prior exceedances is labelled unprecedented in the observed sample; it is never given an invented recurrence interval.
Stock observations use split-adjusted price returns, without dividend reinvestment. Commodities are explicitly labelled ETF price proxies; they do not represent spot commodity prices.
Questions behind the sigma
What does a 3σ move mean?
The period log return is three times the volatility estimated from earlier periods. Sigma is signed: negative for declines and positive for rises.
Why not calculate rarity from a normal distribution?
Market returns have heavy tails and changing volatility. We count actual past absolute sigma exceedances for the same instrument and period.
Does “once every 200 days” predict the next event?
No. It is the number of historical observed periods divided by comparable moves. Events can cluster and the market regime can change.
How much history is required?
At least three years of valid standardized observations, after a one-year volatility warm-up. This normally requires approximately four years of source history.
Are all instruments directly comparable?
The engine is shared, but each instrument has its own prices, calendar, volatility and reference sample. Commodity cards use explicitly labelled ETF proxies.
What happens on quiet days?
The page shows the largest covered standardized move, the complete rarity scale and recent records. Missing data is reported separately from market calm.
For information only. Historical observations are not investment advice and do not predict future moves. A rare move can be followed by another rare move.